A Novel Graph Entropy Minimization Spectral Embedding Framework for Robust Feature Selection in High‐Dimensional Biomedical Data

High‐dimensional datasets with limited samples remain a major challenge in biomedical predictive modeling, as conventional feature selection methods often lack stability and deep learning models require large cohorts for reliable performance. This study proposes Graph Entropy Minimization for Spectral Embedding (GEMS), a novel framework designed to identify compact, discriminative, and nonredundant features by minimizing entropy within spectral embeddings. We validate GEMS on four benchmark cancer datasets spanning three cancer types and two profiling platforms, including a challenging cross‐platform transfer setting. GEMS was evaluated against several established methods, including ReliefF, Mutual Information (MI), HSIC, LASSO, PCA, convolutional neural networks (CNNs), FT‐Transformer, and Attention‐based MLP, using four benchmark cancer datasets: Ovarian, Prostate, Lung GSE75037, and a cross‐platform validation setting based on TCGA‐LUAD and GSE19188. Performance was assessed using accuracy, AUC, F1‐score, PR‐AUC, MCC, and stability metrics. Experimental results showed that GEMS consistently outperformed competing approaches, achieving up to 96.0% ± 1.0% accuracy and an AUC of 0.97 ± 0.01 using approximately 200 selected features. The framework also demonstrated superior feature stability and strong cross‐platform generalization, where deep learning methods showed substantial performance degradation. Biological enrichment analysis confirmed significant associations with established cancer pathways, including PI3K‐AKT and MAPK, supporting the biological relevance and translational potential of the proposed framework.